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How to prove the following identity

  1. Nov 15, 2012 #1
    1. The problem statement, all variables and given/known data

    e_j=g_(jk)e^k

    where e_j is a covariant vector base
    e^k is a a contravariant vector base
    g_(jk) is the covariant metric

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 15, 2012 #2

    HallsofIvy

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    What is the definition of the "covariant metric". How do you go from a covariant to the corresponding contravariant vector and vice-versa?
     
  4. Nov 15, 2012 #3
    Hi, by saying "covariant metic" I mean writing the metric in its covariant form - basically g(contra)=[g(cov)]^(-1)
    you can use the metric to lower/raise an index on a vector component but here e_j and e^k are not components but the actual unit vectors.
     
  5. Nov 15, 2012 #4
    Hi, by saying "covariant metic" I mean writing the metric in its covariant form - basically g(contra)=[g(cov)]^(-1)
    you can use the metric to lower/raise an index on a vector component but here e_j and e^k are not components but the actual unit vectors.
     
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